Combining data and simulated data for space-time fields: application to ozone

This paper presents a theory for modeling random environmental spatial-temporal fields that allows simulated data (numerical-physical model output) to be combined with measurements made at fixed monitoring sites. That theory involves Bayesian hierarchical models that provide temporal forecasts and spatial predictions along with appropriate credibility intervals. A by-product is a method for re-calibrating the simulated data to bring it into line with the measurements for certain applications. While the approach covers a broad domain of potential applications, this paper addresses a field of particular importance, ground level ozone concentrations over the eastern and central USA. A univariate model is developed and illustrated with hourly ozone fields. A multivariate alternative is also provided and illustrated with daily concentration fields. The forecasts and predictions they provide are compared with those from other approaches.